# Transfer-closed characteristicity is transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., transfer-closed characteristic subgroup) satisfying a subgroup metaproperty (i.e., transitive subgroup property)

View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about transfer-closed characteristic subgroup |Get facts that use property satisfaction of transfer-closed characteristic subgroup | Get facts that use property satisfaction of transfer-closed characteristic subgroup|Get more facts about transitive subgroup property

## Definition

Suppose are groups such that is a transfer-closed characteristic subgroup of and is a transfer-closed characteristic subgroup of . Then, is a transfer-closed characteristic subgroup of .

## Facts used

## Proof

### Proof using given facts

The proof follows from facts (1) and (2).

### Hands-on proof

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